Related papers: Compositional Semantics of Finite Petri Nets
We investigate the structural relationship between prefix-free codes over the binary alphabet and a class of unlabeled rooted trees, which we call \emph{symmetric} trees. We establish a canonical correspondence between prefix-free codes and…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set…
Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical formulation of this problem, where operations on state-based…
Can music be represented as a meaningful geometric and topological object? In this paper, we propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the \textit{Tonnetz}. The…
We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…
Sentence encoders play a pivotal role in various NLP tasks; hence, an accurate evaluation of their compositional properties is paramount. However, existing evaluation methods predominantly focus on goal task-specific performance. This…
We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be…
Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often…
Web services growth makes the composition process a hard task to solve. This numerous interacting elements can be adequately represented by a network. Discovery and composition can benefit from the knowledge of the network structure. In…
We propose the Decomposer Networks (DecompNet), a semantic autoencoder that factorizes an input into multiple interpretable components. Unlike classical autoencoders that compress an input into a single latent representation, the Decomposer…
Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is the verification of safety and liveness properties in this model; despite the…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
A desired but challenging property of compiler verification is compositionality, in the sense that the compilation correctness of a program can be deduced incrementally from that of its substructures ranging from statements, functions, and…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Stable event structures, and their duality with prime algebraic domains arising as partial orders of configurations, are a landmark of concurrency theory, providing a clear characterisation of causality in computations. They have been used…
Construction Grammar hypothesizes that knowledge of a language consists chiefly of knowledge of form-meaning pairs (''constructions'') that include vocabulary, general grammar rules, and even idiosyncratic patterns. Recent work has shown…
We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that infinite behaviours may fail to have parallel decompositions at all. Then, we prove that totally normed behaviours always…
Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally…
A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. This paper explores the class of marked Petri nets that…